Eclipsa's reputation/powerlevel is way too high for the show to have her seriously fight Star (or even Moon) anytime soon. Aside from Rhombulus who is a total jobber and will likely be the first threat Eclipsa tries to neutralize, they have no obvious way of stopping her from taking anything she needs by force.
So logically there's one of two ways for the story to write its way out of this:
1) Eclipsa's goals, at least in the short term, can't be accomplished just by her extreme magical power. Common speculation is that she'll be a more sympathetic/tragic villain than Toffee, and her endgame might be something more nuanced and reasonable like enforcing equality of Mewmans and Monsters in Mewni. To that end, she might decide that rather than taking the direct approach and seizing the throne by force, she would instead want to groom Star, the legitimate heir, to rule in her place and shape Mewni according to her ideals.
2) Eclipsa may be not nearly as reckless as Star, and despite her unmatched magical abilities might take a more cautious approach than trying to be a one-woman army. She may take a path similar to Toffee, seeking allies and underlings in pursuit of her long-term goal. She might try to directly rally the monsters to her cause and more directly antagonize Mewni, even if she stays "behind the scenes." She could still plausibly turn several "good guys" sympathetic to her cause, such as Buff Frog and maybe still Star herself.
One very entertaining possibility is that Eclipsa could actually steal the Royal Wand "back" from Star. Star is still dependent on it, so this would severely limit her ability to (ab)use magic and make even ordinary monsters somewhat threatening again.
Eclipsa, in turn, could the grant the Wand to another person to serve as her "apprentice," a classic "dark magical girl" rival for Star who would be a more mid-level threat that they could plausibly defeat. The prime candidate would of course be Jackie.